If you are checking the "Prompt for backup" option in the "During exit" section of "Startup and Exit" in Prefrences, then after you check it, first click "Apply" and only then click "OK'. See if that helps.

The problem appears to be another of the "focus" problems that I have incurred before and never got resolved. The prompt parameter stayed as Yes from yesterday, through a shutdown last night and restart this morning, and all day today. Tonight I was working in a browser window on my 2nd screen, finished up, and reached over and clicked the X to close the TMG window on screen 1, without first giving that window focus. It shut down without prompting for backup, and when I checked the app.ini file, the prompt option was No.

assume currently the prompt is set to Yes. You want to shtdown TMG and you get the prompt/reminder to save. On this prompt at bottom you are asked if this should be repeated the next time. Be sure this is checked (with a hook). Otherwise the prompt is reset to no.

I have no clue what's causing the issue, but I would suggest a work-around if you haven't tried it already (actually, I turned off that prompt years ago in favor of this solution). Put a backup button on the custom toolbar, and you can make a backup with a single click. Not only when you exit, but any time you have put in more data than you would care to have to re-enter.